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3.5 Limits at Infinity

3.5 Limits at Infinity. "The only angle from which to approach a problem is the TRY-Angle". Objective. To evaluate limits as a function approaches infinity. A change in approach. We’ve been looking at limits as they appraoch a certain value x  7, x  -3, x  2,135

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3.5 Limits at Infinity

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  1. 3.5 Limits at Infinity "The only angle from which to approach a problem is the TRY-Angle"

  2. Objective • To evaluate limits as a function approaches infinity

  3. A change in approach • We’ve been looking at limits as they appraoch a certain value • x  7, x  -3, x  2,135 • We can also look as x approaches infinity or negative infinity

  4. Example by chart

  5. Or by graph

  6. Thm: Limits at Infinity • If r is a positive rational number and c is a number then • Also, if x^r is defined when x<0, then

  7. Example

  8. Rewriting

  9. 3 Rules • 1. If the numerator’s exponent is greater than the denominator then the limit is infinity or negative infinity • 2. If the numerator’s exponent is less than the denominator then the limit is zero • 3. If the numerator’s exponent is equal to the denominator then the limit is the ratio of coefficients

  10. Examples

  11. Trig functions

  12. Proof:

  13. Horizontal asymptotes • The line y = L is a h.a. of the graph if:

  14. In other words… • To find h.a. take the limit as a function approaches infinity and/or negative infinity

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